(r+1)(r+4)=3

Solution for (r+1)(r+4)=3 equation:

Simplifying
(r + 1)(r + 4) = 3

Reorder the terms:
(1 + r)(r + 4) = 3

Reorder the terms:
(1 + r)(4 + r) = 3

Multiply (1 + r) * (4 + r)
(1(4 + r) + r(4 + r)) = 3
((4 * 1 + r * 1) + r(4 + r)) = 3
((4 + 1r) + r(4 + r)) = 3
(4 + 1r + (4 * r + r * r)) = 3
(4 + 1r + (4r + r2)) = 3

Combine like terms: 1r + 4r = 5r
(4 + 5r + r2) = 3

Solving
4 + 5r + r2 = 3

Solving for variable 'r'.

Reorder the terms:
4 + -3 + 5r + r2 = 3 + -3

Combine like terms: 4 + -3 = 1
1 + 5r + r2 = 3 + -3

Combine like terms: 3 + -3 = 0
1 + 5r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 5r + -1 + r2 = 0 + -1

Reorder the terms:
1 + -1 + 5r + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5r + r2 = 0 + -1
5r + r2 = 0 + -1

Combine like terms: 0 + -1 = -1
5r + r2 = -1

The r term is 5r.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5r + 6.25 + r2 = -1 + 6.25

Reorder the terms:
6.25 + 5r + r2 = -1 + 6.25

Combine like terms: -1 + 6.25 = 5.25
6.25 + 5r + r2 = 5.25

Factor a perfect square on the left side:
(r + 2.5)(r + 2.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(r + 2.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
r + 2.5 = 2.291287847

Simplifying
r + 2.5 = 2.291287847

Reorder the terms:
2.5 + r = 2.291287847

Solving
2.5 + r = 2.291287847

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = 2.291287847 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = 2.291287847 + -2.5
r = 2.291287847 + -2.5

Combine like terms: 2.291287847 + -2.5 = -0.208712153
r = -0.208712153

Simplifying
r = -0.208712153

Subproblem 2
r + 2.5 = -2.291287847

Simplifying
r + 2.5 = -2.291287847

Reorder the terms:
2.5 + r = -2.291287847

Solving
2.5 + r = -2.291287847

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = -2.291287847 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = -2.291287847 + -2.5
r = -2.291287847 + -2.5

Combine like terms: -2.291287847 + -2.5 = -4.791287847
r = -4.791287847

Simplifying
r = -4.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.208712153, -4.791287847}